I was planning ahead to start a mage and checked out the possible enchantments. To start with, I would assume most of the time the mage is not using weapons or a shield ... at least, that is if he wants to maximize any of the destruction, restoration, etc. spells. That leaves 6 items of gear. If you don't have the dual-enchanting perk, then I'd imagine that the helm, armor, neck and ring would have all destruction or a combination of destruction, conjuration, restoration, etc. That leaves the gloves and boots. The boots seem to be limited to a resist enchant (frost, fire, etc.) and the gloves fortify magicka.
So, picturing a mage with destruction in one hand and restoration in the other ... the mage is starting out at a real disadvantage in survival. I remember starting one, early on, and having tons of trouble surviving a frostbite spider at lvl8.
All this said, it appears that enchanting is the most essential skill to race through to get the double enchanting perk.